Here is what Google Maps shows, as I would go with an RV. To get to the CG in Letchworth SP you want to enter via the Castile entrance, which takes you directly into the CG.
Shared route
From Four Mile Creek State Park to Letchworth State Park - Castile Entrance via NY-63 S.
1 hr 54 min (81 mi)
1 hr 54 min in current traffic
1. Head south
2. Turn left onto NY-18 E
3. Turn right onto Cothran Rd
4. Turn left onto Youngstown Wilson Rd
5. Turn right onto Lutts Rd
6. Turn left onto NY-93 E
7. Turn left onto NY-104 E/NY-93 E
8. Slight right toward Stone Rd
9. Turn left onto NY-31 E
10. Keep right to continue on NY-77 S
11. Turn right onto NY-77 S/Lewiston Rd
12. Turn right to stay on Lewiston Rd
13. Turn left onto NY-63 S
14. Use the left 2 lanes to turn left onto W Main St
15. Turn right onto NY-63 S/Ellicott St
16. Turn right onto NY-246 S
17. Turn right onto NY-39 W/S Main St
18. Turn left onto E Park Rd
19. Turn left onto Denton Corners Rd
20. Arrive at location: Letchworth State Park - Castile Entrance
For the best route in current traffic visit https://goo.gl/maps/ccv2w16ey5S2
PS. We love this park! Give me a shout when you are planning to be there.